Integrable perturbations of conformal field theories and Yetter-Drinfeld modules

Journal Article · Sat Nov 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4902003· OSTI ID:22403045

Bücher, David ^[1]; Runkel, Ingo ^[2]

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1. RTG “Mathematical Structures in Modern Quantum Physics,” Universität Göttingen, Bunsenstr. 3–5, 37073 Göttingen (Germany)
2. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg (Germany)

In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.

• OSTI ID: 22403045
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 11; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BOSONS
COMPACTIFICATION
CONFORMAL INVARIANCE
DISTURBANCES
INTEGRAL CALCULUS
PERTURBATION THEORY
QUANTUM FIELD THEORY
QUANTUM GROUPS